First of all, if you are getting wet when digging a snow cave, you are doing something wrong. The standard uniform is nothing but a polypro base layer, and then Gore-tex or equivalent over it. No insulation, or else you'll get very hot.
Suppose that you dig a standard snow trench. How would you use those poles? If you just lay them flat across the trench and then lay a tarp over, that will begin to work, but it might also collapse if you get enough snow weight on it. Once you've used it, it becomes very hard to excavate the poles out again. Not recommended.
The standard shelter method is to use a snow saw and cut blocks from a hard flat snow surface. Roughly 16" cubes should do it. Cut and remove the blocks in a square pattern, perhaps growing to 8'x8'. Once you've removed one layer of blocks, you might be removing a second layer also. As each block is removed, it is placed around the outside of the 8'x8' square, producing a wind wall. The wind wall ends up being one or two layers high, and you've dug down one or two layers. You use X-C skis, ski poles, fiberglas poles, or whatever to construct an arch over the top layer of the wind wall, and cover that with a Megamid or tarp or whatever you have that is large enough, and anchor down the corners and edges. One leeward corner of the wind wall is excavated to be the door. There should be enough room for about four people to sleep. Tried and true.